Ehrenfest theorem

Ehrenfest theorem - theorem that the time evolution of the expectation value of a quantum observable is proportional to that of the commutator between the observable and the Hamiltonian (plus that of any explicit time dependence of the operator, if any). Article “Ehrenfest theorem” in English Wikipedia has 24 points for quality (as of July 1, 2025). The article contains 11 references and 7 sections.

This article has the best quality in Estonian Wikipedia. However, this article is the most popular in English version.

Since the creation of article “Ehrenfest theorem”, its content was written by 72 registered users of English Wikipedia and edited by 301 registered Wikipedia users in all languages.

The article is cited 39 times in English Wikipedia and cited 450 times in all languages.

The highest Authors Interest rank from 2001:

• Local (English): #36505 in February 2013
• Global: #29861 in June 2006

The highest popularity rank from 2008:

• Local (English): #127753 in March 2019
• Global: #139597 in September 2008

There are 25 language versions for this article in the WikiRank database (of the considered 55 Wikipedia language editions).

The quality and popularity assessment was based on Wikipédia dumps from July 1, 2025 (including revision history and pageviews for previous years).

The table below shows the language versions of the article with the highest quality.

#	Language	Quality grade	Quality score
1	Estonian (et) Ehrenfesti teoreem		28.7424
2	Chinese (zh) 埃倫費斯特定理		24.77
3	English (en) Ehrenfest theorem		24.0063
4	Hebrew (he) משפט ארנפסט		21.2851
5	Catalan (ca) Teorema d'Ehrenfest		15.7953
6	Vietnamese (vi) Định lý Ehrenfest		15.1622
7	Italian (it) Teorema di Ehrenfest		14.9805
8	Ukrainian (uk) Теорема Еренфеста		14.0236
9	Finnish (fi) Ehrenfestin teoreema		13.1405
10	Indonesian (id) Teorema Ehrenfest		12.6373

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The following table shows the most popular language versions of the article.

The most popular language versions of the article "Ehrenfest theorem" in all the time

#	Language	Popularity award	Relative popularity
1	English (en) Ehrenfest theorem		844 765
2	German (de) Ehrenfest-Theorem		222 441
3	Japanese (ja) エーレンフェストの定理		94 818
4	Russian (ru) Теорема Эренфеста		77 914
5	French (fr) Théorème d'Ehrenfest		67 752
6	Spanish (es) Teorema de Ehrenfest		67 179
7	Italian (it) Teorema di Ehrenfest		61 183
8	Chinese (zh) 埃倫費斯特定理		45 204
9	Portuguese (pt) Teorema de Ehrenfest		29 391
10	Polish (pl) Twierdzenie Ehrenfesta		28 238

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The following table shows the language versions of the article with the highest popularity in the last month.

The most popular language versions of the article "Ehrenfest theorem" in June 2025

#	Language	Popularity award	Relative popularity
1	English (en) Ehrenfest theorem		3 313
2	German (de) Ehrenfest-Theorem		902
3	Italian (it) Teorema di Ehrenfest		487
4	Japanese (ja) エーレンフェストの定理		479
5	Russian (ru) Теорема Эренфеста		365
6	French (fr) Théorème d'Ehrenfest		279
7	Spanish (es) Teorema de Ehrenfest		274
8	Polish (pl) Twierdzenie Ehrenfesta		190
9	Chinese (zh) 埃倫費斯特定理		176
10	Korean (ko) 에렌페스트 정리		129

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The following table shows the language versions of the article with the highest Authors’ Interest.

Language versions of the article "Ehrenfest theorem" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.

#	Language	AI award	Relative AI
1	English (en) Ehrenfest theorem		72
2	Italian (it) Teorema di Ehrenfest		40
3	German (de) Ehrenfest-Theorem		36
4	French (fr) Théorème d'Ehrenfest		28
5	Russian (ru) Теорема Эренфеста		17
6	Polish (pl) Twierdzenie Ehrenfesta		16
7	Japanese (ja) エーレンフェストの定理		11
8	Chinese (zh) 埃倫費斯特定理		11
9	Greek (el) Θεώρημα του Έρενφεστ		9
10	Czech (cs) Ehrenfestovy teorémy		8

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The following table shows the language versions of the article with the highest Authors’ Interest in the last month.

Language versions of the article "Ehrenfest theorem" with the highest AI in June 2025

#	Language	AI award	Relative AI
1	Arabic (ar) مبرهنة إيهرينفيست		0
2	Belarusian (be) Тэарэма Эрэнфеста		0
3	Bulgarian (bg) Теорема на Еренфест		0
4	Catalan (ca) Teorema d'Ehrenfest		0
5	Czech (cs) Ehrenfestovy teorémy		0
6	German (de) Ehrenfest-Theorem		0
7	Greek (el) Θεώρημα του Έρενφεστ		0
8	English (en) Ehrenfest theorem		0
9	Spanish (es) Teorema de Ehrenfest		0
10	Estonian (et) Ehrenfesti teoreem		0

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The following table shows the language versions of the article with the highest number of citations.

Language versions of the article "Ehrenfest theorem" with the highest Citation Index (CI)

#	Language	CI award	Relative CI
1	Russian (ru) Теорема Эренфеста		88
2	Polish (pl) Twierdzenie Ehrenfesta		80
3	Japanese (ja) エーレンフェストの定理		61
4	Ukrainian (uk) Теорема Еренфеста		58
5	English (en) Ehrenfest theorem		39
6	Belarusian (be) Тэарэма Эрэнфеста		22
7	French (fr) Théorème d'Ehrenfest		15
8	German (de) Ehrenfest-Theorem		14
9	Chinese (zh) 埃倫費斯特定理		12
10	Hebrew (he) משפט ארנפסט		7

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#	Language	Value
ar	Arabic مبرهنة إيهرينفيست
be	Belarusian Тэарэма Эрэнфеста
bg	Bulgarian Теорема на Еренфест
ca	Catalan Teorema d'Ehrenfest
cs	Czech Ehrenfestovy teorémy
de	German Ehrenfest-Theorem
el	Greek Θεώρημα του Έρενφεστ
en	English Ehrenfest theorem
es	Spanish Teorema de Ehrenfest
et	Estonian Ehrenfesti teoreem
fa	Persian قضیه ارنفست
fi	Finnish Ehrenfestin teoreema
fr	French Théorème d'Ehrenfest
he	Hebrew משפט ארנפסט
id	Indonesian Teorema Ehrenfest
it	Italian Teorema di Ehrenfest
ja	Japanese エーレンフェストの定理
ko	Korean 에렌페스트 정리
pl	Polish Twierdzenie Ehrenfesta
pt	Portuguese Teorema de Ehrenfest
ru	Russian Теорема Эренфеста
sl	Slovenian Ehrenfestov izrek
uk	Ukrainian Теорема Еренфеста
vi	Vietnamese Định lý Ehrenfest
zh	Chinese 埃倫費斯特定理

Best Rank

English: #127753 03.2019

Global: #139597 09.2008

Best Rank

English: #36505 02.2013

Global: #29861 06.2006

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The WikiRank project is intended for automatic relative evaluation of the articles in the various language versions of Wikipedia. At the moment the service allows to compare over 44 million Wikipedia articles in 55 languages. Quality scores of articles are based on Wikipedia dumps from July, 2025. When calculating current popularity and AI of articles data from June 2025 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2025... More information